Opgave 10 opdracht 2

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Tue, 26 Jan 2010 04:36:02 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/26/t1264505795u886cc1dx8w4g1w.htm/, Retrieved Tue, 26 Jan 2010 12:36:40 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Jan/26/t1264505795u886cc1dx8w4g1w.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

24.3 29.4 31.8 36.7 37.1 37.7 39.4 43.3 39.6 34.3 32 29.6 22.3 28.9 31.7 34.2 38.6 37.2 38.8 43.4 38.8 36.3 33 29.2 22.64 28.44 30.14 34.39 36.82 36.74 38.9 42.8 39.09 37.49 33.17 30.98 21.2 27.8 29 35.4 37.5 34.7 38.4 39.9 35.9 34.7 30.4 29 21.5 28 29.3 34.3 36.6 36.2 37.5 41.6 39.4 37.3 32.7 30.7 22.9 29.1 29.5 37.1 37.7 38.4 39.4 40.6 39.7 36.6 32.8 31.6 24.1 30.3 31.8 38.7 37.8 38.4 40.7 43.8 41.5 39.3 35.9 33.4

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.124974553803989 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 31.8 34.5 -2.7 4 36.7 36.5625687047292 0.137431295270773 5 37.1 41.4797441195344 -4.3797441195344 6 37.7 41.33238755242 -3.63238755241994 7 39.4 41.4784315388131 -2.0784315388131 8 43.3 42.9186804846378 0.381319515362208 9 39.6 46.8663357209269 -7.26633572092693 10 34.3 42.2582286564141 -7.95822865641411 11 32 35.9636525810086 -3.96365258100864 12 29.6 33.1682968682631 -3.56829686826305 13 22.3 30.3223505593117 -8.02235055931171 14 28.9 22.0197608777026 6.88023912229745 15 31.7 29.4796156920764 2.22038430792358 16 34.2 32.5571072302325 1.64289276976746 17 38.6 35.2624270210820 3.33757297891796 18 37.2 40.0795387149106 -2.87953871491056 19 38.8 38.3196696488533 0.480330351146698 20 43.4 39.9796987201664 3.42030127983363 21 38.8 45.0071493464888 -6.20714934648879 22 36.3 39.6314136265166 -3.33141362651664 23 33 36.7150716950062 -3.71507169500619 24 29.2 32.9507822675730 -3.75078226757296 25 22.64 28.6820299272671 -6.04202992726712 26 28.44 21.3669299330366 7.07307006696344 27 30.14 28.0508837086797 2.08911629132033 28 34.39 30.0119700850321 4.37802991496793 29 36.82 34.8091124201957 2.01088757980430 30 36.74 37.4904221982317 -0.750422198231725 31 38.9 37.3166385188431 1.58336148115689 32 42.8 39.6745184134611 3.12548158653888 33 39.09 43.9651240801614 -4.87512408016138 34 37.49 39.6458576235041 -2.15585762350415 35 33.17 37.7764302789418 -4.60643027894179 36 30.98 32.8807437102019 -1.90074371020185 37 21.2 30.4531991131236 -9.25319911312364 38 27.8 19.5167846827015 8.28321531729845 39 29 27.1519758210433 1.84802417895671 40 35.4 28.5829318182274 6.81706818177262 41 37.5 35.8348918724958 1.66510812750422 42 34.7 38.142988017766 -3.44298801776602 43 38.4 34.9127021264932 3.48729787350676 44 39.9 39.0485256222163 0.85147437778366 45 35.9 40.6549382526554 -4.75493825265538 46 34.7 36.0606919661643 -1.36069196616425 47 30.4 34.6906400948282 -4.29064009482821 48 29 29.8544192634435 -0.854419263443546 49 21.5 28.3476385972332 -6.84763859723316 50 28 19.9918580189330 8.00814198106703 51 29.3 27.4926719898158 1.80732801018419 52 34.3 29.0185420014660 5.28145799853396 53 36.6 34.6785898582673 1.92141014173268 54 36.2 37.2187172334048 -1.01871723340482 55 37.5 36.6914035017076 0.808596498292374 56 41.6 38.0924574882892 3.50754251171082 57 39.4 42.6308110486388 -3.23081104863876 58 37.3 40.0270418794101 -2.72704187941014 59 32.7 37.5862310373261 -4.88623103732606 60 30.7 32.3755764936530 -1.67557649365304 61 22.9 30.1661720689943 -7.2661720689943 62 29.1 21.4580854568087 7.64191454319127 63 29.5 28.6131303170523 0.88686968294773 64 37.1 29.1239664599609 7.97603354003905 65 37.7 37.720767692753 -0.0207676927529761 66 38.4 38.3181722596176 0.0818277403823586 67 39.4 39.0283986449607 0.371601355039289 68 40.6 40.0748393584997 0.5251606415003 69 39.7 41.3404710753466 -1.64047107534662 70 36.6 40.2354539346768 -3.63545393467682 71 32.8 36.6811147013156 -3.88111470131564 72 31.6 32.3960741232566 -0.79607412325661 73 24.1 31.0965851149077 -6.99658511490772 74 30.3 22.7221900120205 7.5778099879795 75 31.8 29.8692234340796 1.93077656592036 76 38.7 31.6105213739007 7.08947862609926 77 37.8 39.3965258019004 -1.59652580190041 78 38.4 38.2970007021713 0.102999297828653 79 40.7 38.9098729934596 1.79012700654039 80 43.8 41.4335933173545 2.36640668264553 81 41.5 44.8293339366369 -3.32933393663686 82 39.3 42.1132519134412 -2.8132519134412 83 35.9 39.5616670108207 -3.66166701082066 84 33.4 35.7040518099646 -2.30405180996457 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 32.916103963073 24.5679892224295 41.2642187037164 86 32.4322079261459 19.8667900453352 44.9976258069567 87 31.9483118892189 15.6151224223613 48.2815013560765 88 31.4644158522919 11.5014994216579 51.4273322829259 89 30.9805198153649 7.41568272577432 54.5453569049554 90 30.4966237784378 3.30654139793398 57.6867061589417 91 30.0127277415108 -0.852982821933644 60.8784383049553 92 29.5288317045838 -5.07829228763902 64.1359556968066 93 29.0449356676568 -9.3784994326798 67.4683707679933 94 28.5610396307297 -13.7590625436191 70.8811418050785 95 28.0771435938027 -18.2232023897495 74.3774895773549 96 27.5932475568757 -22.7727160805715 77.9592111943229

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/26/t1264505795u886cc1dx8w4g1w/1fqnz1264505760.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264505795u886cc1dx8w4g1w/1fqnz1264505760.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264505795u886cc1dx8w4g1w/2j77u1264505760.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264505795u886cc1dx8w4g1w/2j77u1264505760.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264505795u886cc1dx8w4g1w/3ktsp1264505760.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264505795u886cc1dx8w4g1w/3ktsp1264505760.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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